Math  /  Algebra

QuestionUsing the change of base formula, the expression log522log523\frac{\log _{5} 22}{\log _{5} 23} can also be written as log2223\log _{22} 23 log23225\frac{\log _{23} 22}{5} log2322\log _{23} 22 log52223\frac{\log _{5} 22}{23}

Studdy Solution
Recognize that the simplified expression log1022log1023\frac{\log_{10} 22}{\log_{10} 23} is equivalent to log2322\log_{23} 22 using the change of base formula again.
Thus, the expression log522log523\frac{\log_{5} 22}{\log_{5} 23} can be rewritten as:
log2322\log_{23} 22
The correct answer is:
log2322\boxed{\log_{23} 22}

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